ABC is a right-angled triangle and O is the mid-point of the side opposite to the right angle. Explain why O is equidistant from A,B and C. (The dotted lines are drawn additionally to help you).

NCERT - Mathematics

Book: NCERT - Mathematics

Chapter: 3. Understanding Quadrilaterals

Subject: Maths - Class 8^th

Q. No. 6 of Exercises 3.4

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6

ABC is a right-angled triangle and O is the mid-point of the side opposite to the right angle. Explain why O is equidistant from A,B and C. (The dotted lines are drawn additionally to help you).

Draw lines AD and DC such that AD||BC, AB||DC

AD = BC, AB = DC

ABCD is a rectangle as opposite sides are equal and parallel to each other and all the interior angles are of 90^o

In a rectangle, diagonals are of equal length and also these bisect each other

Hence, AO = OC = BO = OD

Thus, O is equidistant from A, B, and C

6

Chapter Exercises

Exercises 3.1

Exercises 3.2

Exercises 3.3

Exercises 3.4

1

State whether True or False
(a) All rectangles are squares

(b) All rhombuses are parallelograms

(c) All squares are rhombuses and also rectangles

(d) All squares are not parallelograms

(e) All kites are rhombuses

(f) All rhombuses are kites

(g) All parallelograms are trapeziums

(h) All squares are trapeziums

2

Identify all the quadrilaterals that have.
(a) Four sides of equal length

(b) Four right angles

3

Explain how a square is
(i) a quadrilateral

(ii) a parallelogram
(iii) a rhombus

(iv) a rectangle

4

Name the quadrilaterals whose diagonals
(i) Bisect each other

(ii) Are perpendicular bisectors of each other

(iii) Are equal

5

Explain why a rectangle is a convex quadrilateral

6

ABC is a right-angled triangle and O is the mid-point of the side opposite to the right angle. Explain why O is equidistant from A,B and C. (The dotted lines are drawn additionally to help you).